Question: Solve for $x$ and $y$ using elimination. ${5x+y = 19}$ ${-2x-y = -10}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $3x = 9$ $\dfrac{3x}{{3}} = \dfrac{9}{{3}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {5x+y = 19}\thinspace$ to find $y$ ${5}{(3)}{ + y = 19}$ $15+y = 19$ $15{-15} + y = 19{-15}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {-2x-y = -10}\thinspace$ and get the same answer for $y$ : ${-2}{(3)}{ - y = -10}$ ${y = 4}$